Estimates for Overshooting an Arbitrary Boundary by a Random Walk and Their Applications

DOI10.1137/S0040585X97977537zbMath0969.60074OpenAlexW2009517300MaRDI QIDQ2711118

Aleksandr A. Borovkov, Sergeĭ Georgievich Foss

Publication date: 2 May 2001

Published in: Theory of Probability & Its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s0040585x97977537

zbMATH Keywords

uniform integrabilityMarkov chainrandom walksequence of random variablesnonlinear boundaryasymptotic homogeneitytime and value of the first overshoot

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50) Probability distributions: general theory (60E05) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Applications of Markov renewal processes (reliability, queueing networks, etc.) (60K20)

Related Items (11)

Asymptotics for the moments of the overshoot and undershoot of a random walk ⋮ Asymptotic expansions of defective renewal equations with applications to perturbed risk models and processor sharing queues ⋮ Estimates for the overshoot of a random walk with negative drift and non-convolution equivalent increments ⋮ The Seneta-Heyde scaling for the branching random walk ⋮ Upper Bounds for the Maximum of a Random Walk with Negative Drift ⋮ The key renewal theorem for a transient Markov chain ⋮ The Uniform Asymptotics of the Overshoot of a Random Walk with Light-Tailed Increments ⋮ Uniform renewal theory with applications to expansions of random geometric sums ⋮ Renewal theorems and stability for the reflected process ⋮ The Uniform Local Asymptotics of the Overshoot of a Random Walk with Heavy-Tailed Increments ⋮ The probability of exceeding a high boundary on a random time interval for a heavy-tailed random walk

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